There quantities P,Q and R are such that P varies as the square root of R.Given that P=20 when Q=5 and R=9,find P when Q=7 and R=25
To find the relationship between P, Q, and R, we need to establish the pattern from the given information.
We are told that P varies as the square root of R, which means that P = k√R, where k is a constant.
Substituting the given values, we have:
20 = k√9
20 = 3k
k = 20/3
Now we can find P when Q = 7 and R = 25:
P = (20/3)√25
P = (20/3) * 5
P = (100/3)
P ≈ 33.333
Therefore, when Q = 7 and R = 25, P ≈ 33.333.
To find the value of P when Q=7 and R=25, we can use the given information that P varies as the square root of R and the initial condition P=20 when Q=5 and R=9.
Let's first find the constant of variation, k.
Using the initial condition:
P = k * √R
20 = k * √9
Square both sides to eliminate the square root:
400 = 9k^2
Divide both sides by 9:
k^2 = 400/9
Take the square root of both sides:
k = √(400/9) = 20/3
Now, we can substitute the values of Q and R into the equation to find P:
P = (20/3) * √R
When Q=7 and R=25:
P = (20/3) * √25
Simplify:
P = (20/3) * 5
Multiply:
P = 100/3
Therefore, when Q=7 and R=25, P is equal to 100/3.